This technical note studies selected reset resource trade-offs for a fixed source-tagged quantum-record apparatus at independently known source length m = 65. It preserves the already published target preparation, complete-reader initialization, calibration and acquisition results as inherited interfaces. For exact unitary reset with a pure initialized environment and arbitrary inert-reference correlations, the environment dimension must be at least the 131-dimensional source dimension. Under the staged-isolation contract in which a dedicated source bank is the only system allowed to retain the source label during the source stage, five qutrits are necessary among qutrit tensor banks because 3^4 < 131 <= 3^5. An explicit five-qutrit encoded-bank construction attains that count. The paper compares two constructions satisfying the same full-joint reset interface. A nearest-neighbor-transport circuit uses 65 source qutrits and 2,159 finite slots; its source stage combines neighboring transfers with 65 globally vacuum-conditioned extraction pulses. An encoded-bank circuit uses five qutrits and 15 slots, but assumes one nonlocal, coherently phased 130-block all-site extraction Hamiltonian. Under the declared supply, control, generator-error and isolation conditions, the sufficient reset bounds are below 0.000083661 and 0.000081959, respectively, and both remain within the existing downstream initialization allocation. The contribution is an apparatus-specific comparison of selected feasible points in environment dimension, control connectivity, pulse count, strength and slew, elapsed model time, calibration burden and complete-input error. It does not prove a Pareto frontier, a general reset resource theory, a local synthesis of the encoded Hamiltonian, an approximate or catalytic optimum, an all-length theorem or practical implementation.
This technical note studies selected reset resource trade-offs for a fixed source-tagged quantum-record apparatus at independently known source length m = 65. It preserves the already published target preparation, complete-reader initialization, calibration and acquisition results as inherited interfaces. For exact unitary reset with a pure initialized environment and arbitrary inert-reference correlations, the environment dimension must be at least the 131-dimensional source dimension. Under the staged-isolation contract in which a dedicated source bank is the only system allowed to retain the source label during the source stage, five qutrits are necessary among qutrit tensor banks because 3^4 < 131 <= 3^5. An explicit five-qutrit encoded-bank construction attains that count. The paper compares two constructions satisfying the same full-joint reset interface. A nearest-neighbor-transport circuit uses 65 source qutrits and 2,159 finite slots; its source stage combines neighboring transfers with 65 globally vacuum-conditioned extraction pulses. An encoded-bank circuit uses five qutrits and 15 slots, but assumes one nonlocal, coherently phased 130-block all-site extraction Hamiltonian. Under the declared supply, control, generator-error and isolation conditions, the sufficient reset bounds are below 0.000083661 and 0.000081959, respectively, and both remain within the existing downstream initialization allocation. The contribution is an apparatus-specific comparison of selected feasible points in environment dimension, control connectivity, pulse count, strength and slew, elapsed model time, calibration burden and complete-input error. It does not prove a Pareto frontier, a general reset resource theory, a local synthesis of the encoded Hamiltonian, an approximate or catalytic optimum, an all-length theorem or practical implementation.
We study exact reference-preserving reset as an information-transfer task in a finite tagged-source model. A declared local-qutrit realization admits a depth-one parallel source-to-bank unitary:65 pair-local exchanges reset the complete source carrier on a pure-zero bank while transferringeach source basis label to an orthogonal bank record and each source matrix unit coherently to thecorresponding bank matrix unit. We propagate this identity through an inherited work-replacementinterface and a complete-joint error contract, deriving a channel-wise calibration theorem thatcharges coefficient, timing, axis, cross-talk, leakage and bank-dynamics errors against one globalallowance. For admitted complete inputs whose nominal post-replacement source-bank comparisonis supported on the vacuum-plus-one-excitation sector with a zero bank, a per-port peak 218J givesa sufficient reset bound below 10−4 at source length 65 and preserves the existing reader allocation,while requiring 65 local ports, an aggregate peak 65·218J, and stringent joint calibration. Conversely,an ε-reset of a d-dimensional input with a pure blank environment requires environment dimensionat least ⌈d(1−ε)⌉. At ε= 10−4 the 131-dimensional tagged source still requires 131 environmentdimensions. Combining this rank bound with circuit causal cones yields memory-dependent depthlower bounds; combining environment distinguishability with a supplied positive-constant Lieb–Robinson profile yields a conditional reset-time lower bound that is nontrivial only when the profileseparation term is positive. The results quantify a memory–locality–calibration trade-off in onedeclared architecture. They do not establish optimal hardware, practical supplier generation, anautonomous repeated-use service, or a universal tight reset speed.
A calibrated quantum-record test can require both a global target state and a commoncomplete reader input, neither of which is certified by accessible marginal data. We construct theseinputs for the specified source-tagged model at an independently known source length m= 65. Thepublished joint-input work/source reset is followed by 37 finite swaps with fresh reader qubits and a69-slot target sequence: coherent work-label creation, globally conditioned tag injection, and 64neighboring source transfers. The control-only sequence prepares the exact far-target cat or itssigned partner with the required common phase. A retained random sign produces the comparisonmixture without postselection. Full-state comparisons include consumed supplies and arbitraryinitial correlations with exactly inert retained memory. The original clock, holding terms, sourcehopping, both port directions and either actual law, h= 0 or h= J/25, remain active throughout.The constructed initialization fits the existing 1/4000 allowance; target delivery has sufficienterror below 0.004816692 <1/200. With separate complete-interval generator and endpoint-effectallowances, each target response differs from its nominal value by less than 0.007816692 <1/125.The same reader initialization supplies the published reference-preparation interface. The resultis a conditional single-delivery construction: it consumes 37 fresh pure reader qubits, requirespreparation access through site 65 and additional globally conditioned controls, and inherits anextremely costly reset. Application to repeated acquisition still requires almost-sure conditionalsupply and error bounds; practical feasibility and uniform passing power are not established.
We construct a source-matched reference calibration for distinguishing the coherent law h = 0 from the specified added generator h = J/25 in a finite quantum-record model. A complete-carrier transfer bound connects an accessible reference contrast to a delayed target contrast while retaining the original drift and actual law. On reference coverage and measured admission, restricting both hypotheses by the same observed reference band yields a directed target-set separation of at least 0.0071230619 whenever both compatible classes are nonempty. Rival worlds may have different admitted nuisance parameters. The constants are uniform over independently known finite lengths m >= 65, with tag 65, access prefix 1:32 and target deadline 25.02/J. Finite reference preparation and work/source reset satisfy the declared response budgets. Reset acts on the actual joint input and consumed supply, with the retained reference R exactly inert. It does not assign a universal reduced channel to correlated supplies. Under almost-sure conditional resource and supply bounds, the comparison extends to history-dependent acquisition. A prespecified rule, including abstention below the calibration threshold, has each-law unconditional wrong-declaration probability at most 2 exp(-6) + exp(-85/16) < 0.01. This is neither a posterior probability nor an error bound conditional on admission. The statistical step uses standard bounded-martingale concentration. Global target states and specified auxiliary supplies remain resources. Reset requires additional globally conditioned controls and has very large finite costs. The result is a conditional theorem for the two declared laws; it does not establish practical implementation or a unique diagnosis of fundamental collapse. A supporting Lean 4 companion contains 85 theorem declarations and 30 supporting definitions across Calibration, Operations and Risk. It provides checked scalar, sufficient-bound, resource-arithmetic and finite-history risk consequences under explicit premises. The companion has an executed Linux preflight and accepted returned macOS compilation, named-type and transitive-axiom evidence. The quantum constructions and conditional moment, filtration, tower and tail derivations remain written proofs or external premises; this is not an end-to-end formalization of the physical theorem chain. The original checked companion targeted author v0.4 and is carried forward unchanged, with its scope and execution chronology preserved.
A quantum record can have locally accessible populations while its distinguishing phase remains correlated with a distant source. We study this access boundary in a specified finite recording apparatus with a returning, vacuum/one-excitation source. Source-position weights give finite-time cutoff bounds without removing any physical hopping or return coupling. For an initially far-tagged record and its incoherent mixture, every reader in a declared position-preserving local-control class obeys a phase-visibility envelope and a necessary access-time inequality. A separate finite local probe shows why that state-discrimination limit is not an unrestricted limit on distinguishing two dynamical laws: fresh local coherence can reveal a stipulated added dephaser without recovering the old record phase. We construct a bounded, degree-three reader accessing only source positions 1–32. With the initial tag fixed at position 65, exact finite-source arrival certificates and an analytical tail comparison yield recovery uniformly over every finite total source length at least 65. Accessible control faults are charged against the arrived signed-phase norm, while source-moving drift is charged against the full norm. At the fixed deadline 25.02/J, the matched phase-dependent difference between coherent and archive-gated dynamics exceeds 0.005, including the stated simultaneous control faults and four additional absolute response allowances of 0.008 each. Complementary results cover a vacuum-ready source and a stronger endpoint-prepared finite example. The conclusions are conditional on the supplied model, preparations, common realized controls and calibration bounds. They are not a switchable-fundamental-law experiment, a nuisance-independent classifier, an optimal-speed theorem or an end-to-end formal verification. The supporting Lean companion contains 59 declarations in eight modules with accepted returned Mac compilation, type and axiom evidence; physical analytical interfaces remain explicit hypotheses or outside that subset. The deposit files include the main manuscript, technical supplement and full research/reproduction package.
How much internal quantum memory is needed to reproduce a stationary stochastic process, and how does reducing that memory change the environmental resources required when output records are retained? This paper establishes exact quantum-source constructions and resource bounds under explicitly specified readout and retained-output conditions. A general completion theorem identifies the minimum Hilbert-space dimension for stationary triple data in the orthogonal-current-symbol source class: it equals the sum of the complex positive-semidefinite ranks of the middle-symbol slices. An attaining construction reproduces the entire canonical stationary order-two process. For the delayed trine process, the minimum classical hidden Markov model requires nine states at every non-independent parameter value. Quantum instruments reproduce the same complete output law using four-dimensional memory throughout the parameter range, with four dimensions proved necessary in a certified low-noise regime and three dimensions both sufficient and necessary on an explicit high-noise interval. The paper then separates reusable memory dimension from environmental dilation cost. On the certified high-noise interval, the exact one-step Pareto frontier consists of a three-dimensional source with recorded-channel Choi rank nine and a four-dimensional source with rank three. Here, Choi rank measures the minimum initially pure environmental remainder dimension for the channel retaining both the emitted classical symbol and final quantum memory. A separate mixed-support qutrit construction at noise parameter 0.99 improves complete-history costs and gives upper bounds close to universal lower bounds. These results show why optimizing a single step need not optimize a retained multi-step history. The analysis also distinguishes complete channels, fixed-input states and archive-only outputs, and demonstrates how access to a retained reference can distinguish generators with identical passive output statistics. Full-word proofs, algebraic complete-positivity certificates, a technical companion and reproducibility materials accompany the results. The exact intermediate memory boundary and complete-history optimum remain open. All results use standard quantum probabilities and apply to the stated operational resource models; they do not establish total hardware, energy or thermodynamic minima.
A source-inclusive coherence observable is useful only when its measurement resources are admitted. This preprint constructs a bounded local reader for the conserved exchange observable of a specified finite quantum-record apparatus. A degree-three graph uses one independently prepared probe, twenty relays with arbitrary joint states, and finite-duration two-register extraction and full-SWAP interactions. The original apparatus Hamiltonian and an independently added archive-gated process remain active throughout their respective implementations. A prefix-dependent control-frame comparison, symmetry-resolved effect estimate, and explicit gain, phase and finite-slew waveform bounds yield a sufficient response separation greater than 0.005139889 for the stated fixed, fully accessible sixteen-position source and remaining response-error budgets. This is a conditional mathematical result, not measured hardware calibration, a partial-source-access theorem, or a unique diagnosis or derivation of fundamental collapse. The package contains the main manuscript, technical supplement, editable LaTeX, direct numerical reproduction sources, and accepted returned Mac evidence for 56 paper-specific supporting Lean declarations. That subset verifies selected algebra, scalar inequalities and the actual-constant numerical expression; it does not formalize the full physical/continuous-time theorem end-to-end. Separate-session AI review, numerical reproduction and returned kernel evidence are distinguished. Author-owned manuscripts, documentation and mathematical data are CC BY 4.0; newly authored numerical and Lean software is MIT. Predecessor and third-party notices remain unchanged; the reproduction package contains the licence map. No external funding; no competing interests declared. Public preprint v1.0; edition date 18 October 2026; DOI 10.5281/zenodo.23442579.